Time-Optimal Gate-Traversing Planner for Autonomous Drone Racing

In drone racing, the time-minimum trajectory is affected by the drone's capabilities, the layout of the race track, and the configurations of the gates (e.g., their shapes and sizes). However, previous studies neglect the configuration of the gates, simply rendering drone racing a waypoint-passing task. This formulation often leads to a conservative choice of paths through the gates, as the spatial potential of the gates is not fully utilized. To address this issue, we present a time-optimal planner that can faithfully model gate constraints with various configurations and thereby generate a more time-efficient trajectory while considering the single-rotor-thrust limits. Our approach excels in computational efficiency which only takes a few seconds to compute the full state and control trajectories of the drone through tracks with dozens of different gates. Extensive simulations and experiments confirm the effectiveness of the proposed methodology, showing that the lap time can be further reduced by taking into account the gate's configuration. We validate our planner in real-world flights and demonstrate super-extreme flight trajectory through race tracks.

A Spatial-Temporal Deformable Attention based Framework for Breast Lesion Detection in Videos

Detecting breast lesion in videos is crucial for computer-aided diagnosis. Existing video-based breast lesion detection approaches typically perform temporal feature aggregation of deep backbone features based on the self-attention operation. We argue that such a strategy struggles to effectively perform deep feature aggregation and ignores the useful local information. To tackle these issues, we propose a spatial-temporal deformable attention based framework, named STNet. Our STNet introduces a spatial-temporal deformable attention module to perform local spatial-temporal feature fusion. The spatial-temporal deformable attention module enables deep feature aggregation in each stage of both encoder and decoder. To further accelerate the detection speed, we introduce an encoder feature shuffle strategy for multi-frame prediction during inference. In our encoder feature shuffle strategy, we share the backbone and encoder features, and shuffle encoder features for decoder to generate the predictions of multiple frames. The experiments on the public breast lesion ultrasound video dataset show that our STNet obtains a state-of-the-art detection performance, while operating twice as fast inference speed. The code and model are available at https://github.com/AlfredQin/STNet.

Open Problem: Optimal Best Arm Identification with Fixed Budget

Best arm identification or pure exploration problems have received much attention in the COLT community since Bubeck et al. (2009) and Audibert et al. (2010). For any bandit instance with a unique best arm, its asymptotic complexity in the so-called fixed-confidence setting has been completely characterized in Garivier and Kaufmann (2016) and Chernoff (1959), while little is known about the asymptotic complexity in its "dual" setting called fixed-budget setting. This note discusses the open problems and conjectures about the instance-dependent asymptotic complexity in the fixed-budget setting.

Model Predictive Spherical Image-Based Visual Servoing On $SO(3)$ for Aggressive Aerial Tracking

This paper presents an image-based visual servo control (IBVS) method for a first-person-view (FPV) quadrotor to conduct aggressive aerial tracking. There are three major challenges to maneuvering an underactuated vehicle using IBVS: (i) finding a visual feature representation that is robust to large rotations and is suited to be an optimization variable; (ii) keeping the target visible without sacrificing the robot's agility; and (iii) compensating for the rotational effects in the detected features. We propose a complete design framework to address these problems. First, we employ a rotation on $SO(3)$ to represent a spherical image feature on $S^{2}$ to gain singularity-free and second-order differentiable properties. To ensure target visibility, we formulate the IBVS as a nonlinear model predictive control (NMPC) problem with three constraints taken into account: the robot's physical limits, target visibility, and time-to-collision (TTC). Furthermore, we propose a novel attitude-compensation scheme to enable formulating the visibility constraint in the actual image plane instead of a virtual fix-orientation image plane. It guarantees that the visibility constraint is valid under large rotations. Extensive experimental results show that our method can track a fast-moving target stably and aggressively without the aid of a localization system.

Contextual Information-Directed Sampling

Information-directed sampling (IDS) has recently demonstrated its potential as a data-efficient reinforcement learning algorithm. However, it is still unclear what is the right form of information ratio to optimize when contextual information is available. We investigate the IDS design through two contextual bandit problems: contextual bandits with graph feedback and sparse linear contextual bandits. We provably demonstrate the advantage of contextual IDS over conditional IDS and emphasize the importance of considering the context distribution. The main message is that an intelligent agent should invest more on the actions that are beneficial for the future unseen contexts while the conditional IDS can be myopic. We further propose a computationally-efficient version of contextual IDS based on Actor-Critic and evaluate it empirically on a neural network contextual bandit.

Adaptivity and Confounding in Multi-Armed Bandit Experiments

We explore a new model of bandit experiments where a potentially nonstationary sequence of contexts influences arms' performance. Context-unaware algorithms risk confounding while those that perform correct inference face information delays. Our main insight is that an algorithm we call deconfounted Thompson sampling strikes a delicate balance between adaptivity and robustness. Its adaptivity leads to optimal efficiency properties in easy stationary instances, but it displays surprising resilience in hard nonstationary ones which cause other adaptive algorithms to fail.

An Analysis of Ensemble Sampling

Ensemble sampling serves as a practical approximation to Thompson sampling when maintaining an exact posterior distribution over model parameters is computationally intractable. In this paper, we establish a Bayesian regret bound that ensures desirable behavior when ensemble sampling is applied to the linear bandit problem. This represents the first rigorous regret analysis of ensemble sampling and is made possible by leveraging information-theoretic concepts and novel analytic techniques that may prove useful beyond the scope of this paper.

Best Arm Identification with a Fixed Budget under a Small Gap

We consider the fixed-budget best arm identification problem in the multi-armed bandit problem. One of the main interests in this field is to derive a tight lower bound on the probability of misidentifying the best arm and to develop a strategy whose performance guarantee matches the lower bound. However, it has long been an open problem when the optimal allocation ratio of arm draws is unknown. In this paper, we provide an answer for this problem under which the gap between the expected rewards is small. First, we derive a tight problem-dependent lower bound, which characterizes the optimal allocation ratio that depends on the gap of the expected rewards and the Fisher information of the bandit model. Then, we propose the "RS-AIPW" strategy, which consists of the randomized sampling (RS) rule using the estimated optimal allocation ratio and the recommendation rule using the augmented inverse probability weighting (AIPW) estimator. Our proposed strategy is optimal in the sense that the performance guarantee achieves the derived lower bound under a small gap. In the course of the analysis, we present a novel large deviation bound for martingales.

Optimal Simple Regret in Bayesian Best Arm Identification

We consider Bayesian best arm identification in the multi-armed bandit problem. Assuming certain continuity conditions of the prior, we characterize the rate of the Bayesian simple regret. Differing from Bayesian regret minimization (Lai, 1987), the leading factor in Bayesian simple regret derives from the region where the gap between optimal and sub-optimal arms is smaller than $\sqrt{\frac{\log T}{T}}$. We propose a simple and easy-to-compute algorithm with its leading factor matches with the lower bound up to a constant factor; simulation results support our theoretical findings.

Policy Choice and Best Arm Identification: Comments on "Adaptive Treatment Assignment in Experiments for Policy Choice"

Adaptive experimental design for efficient decision-making is an important problem in economics. The purpose of this paper is to connect the "policy choice" problem, proposed in Kasy and Sautmann (2021) as an instance of adaptive experimental design, to the frontiers of the bandit literature in machine learning. We discuss how the policy choice problem can be framed in a way such that it is identical to what is called the "best arm identification" (BAI) problem. By connecting the literature, we identify that the asymptotic optimality of policy choice algorithms tackled in Kasy and Sautmann (2021) is a long-standing open question in the literature. While Kasy and Sautmann (2021) presents an interesting and important empirical study, unfortunately, this connection highlights several major issues with the theoretical results. In particular, we show that Theorem 1 in Kasy and Sautmann (2021) is false. We find that the proofs of statements (1) and (2) of Theorem 1 are incorrect. Although the statements themselves may be true, they are non-trivial to fix. Statement (3), and its proof, on the other hand, is false, which we show by utilizing existing theoretical results in the bandit literature. As this question is critically important, garnering much interest in the last decade within the bandit community, we provide a review of recent developments in the BAI literature. We hope this serves to highlight the relevance to economic problems and stimulate methodological and theoretical developments in the econometric community.